How does one define a sigmoidal function

I am trying to model a 'perturbation function' and I finally arrive at a S-shaped graph,which I later found was called a 'sigmoid'. Is a sigmoid defined based on its inflection point? How does one classify a curve as a 'sigmoid'?
Can i say that a certain function f is a sigmoid just because it has a S-shaped curve?What about skewed S-shaped curves?Are they sigmoids also?
What are the constraints?